The True Retention Time

Because of the lack of knowledge concerning the detailed processes taking place in a g.I.c. column, the present-day theories cannot hope to unravel the problems associated with peak asymmetry. Possible causes that have been given by various workers - - including eddy diffusion in packed columns, nonequilibria between phases, sample size, surface heterogeneity, and non-zero response time of the detecting system. 

Many workers have discussed the first time moment or centre of gravity of a chromatographic peak undergoing elution. In the absence of longitudinal or eddy diffusion this property has been shown to be equal to the ideal thermodynamic retention time for zero-pressure-drop columns. More recently, theories regarding the first time moment have been extended by Hicks and by Buffham to include pressure-drop columns and the first time moment has been related to thermodynamic properties. Buflfham used the mean residence time t which is equivalent to the first time moment  

It is interesting that the first time moment for systems which do not include longitudinal or eddy diffusion has been considered to be independent of the kinetics of equilibration between the phases.  

The problem of locating the true retention volume is, however, usually important only for solutes which have short residence times and have very asymmetric peaks. It is only then that the peak avera retention times differ significantly from the peak-maximum, peak-tangent, peak-half-area, or mean-residence retention time. 

Surface Adsorption Effects.—Surface adsorption is perhaps the most important limitation of the g.l.c. method for determining activity coefiicients. Martin  

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When a peak is not symmetrical, the asymmetry factor is calculated via As = A/B, as defined (in Fig. 3) by drawing a line parallel to the baseline at 10% of peak height. With non-symmetrical peaks, it is necessary to use statistical moments. The zero moment, M0 = f tZ h(t) dt, is the peak height at time t. The first moment, Mt f vQ th(t) dt, expresses the true retention time as... 

The drawings incorporate also points and arrows. The points show the true peak height (and the true retention time as well). In cases of poor resolution it is impossible to set this point intuitively to the true position which is often below the sum curve. The arrows show the positions at which both peaks are separated into fractions of equal purity by preparative chromatography. The number above each arrow indicates the percentage purity level attained. These numbers, however, are only true if the ratio between the amount of material and the signal (peak height as... 

Ramos et al. [13] first separated the individual spectra of benzo[b]fluoranthene and benzo[k]fluoranthene or chrysene and benz[a]anthracene from each other in a purposely created co-eluting peak of mixtures of each of the two pairs of PAHs. They were then able to deconvolute the individual spectra from a mixture of the isomers benzo[e]pyrene, benzo[b]fluoranthene, and benzo[k]fluoranthene in a similar fashion. In all cases they purposely generated peaks with severe overlap (greater than 90 % of each peak co-eluting with the other components) to show the power of deconvolution. Tauler et al. described another algorithm to deconvolute the individual spectra in co-eluting peaks and reviewed similar efforts by others. Multivariate curve resolution has been used as an alternative approach for peak deconvolution. It can identify minor impurity peaks and yield the true retention times [14, 15]. 

The True Retention Time.— Existing theories of g.I.c. predict a unique retention time. Experimentally, however, a peak spread is observed, so it is necessary to speculate where on this peak the true retention time may be found. Figure 1 illustrates some of the peak properties that have been used to define this true retention time. The peak initial time /j and peak final time are determined from the intersection of the base-line time with the tangents to the leading edge... 

If the mobile phase is a liquid, and can be considered incompressible, then the volume of the mobile phase eluted from the column, between the injection and the peak maximum, can be easily obtained from the product of the flow rate and the retention time. For more precise measurements, the volume of eluent can be directly measured volumetrically by means of a burette or other suitable volume measuring vessel that is placed at the end of the column. If the mobile phase is compressible, however, the volume of mobile phase that passes through the column, measured at the exit, will no longer represent the true retention volume, as the volume flow will increase continuously along the column as the pressure falls. This problem was solved by James and Martin [3], who derived a correction factor that allowed the actual retention volume to be calculated from the retention volume measured at the column outlet at atmospheric pressure, and a function of the inlet/outlet pressure ratio. This correction factor can be derived as follows. 

Another serious error can occur if it is known that there are two peaks which are unresolved, and the retention time of the maximum of the envelope is taken as the mean retention time of the two isomers. This measurement can only be true if the peaks are absolutely symmetrical and the two peaks are of equal height. The effect of different,proportions of each isomer on the retention time of the composite envelope is shown in Figure 3. It is seen that the position of the peak maximum of the composite envelope is significantly different from the mean of the retention times of the individual peaks. 

Results obtained by Wirtz and Dague with a systemic residence time of 12 hours are shown in Figure 47, where their systemic residence time , also called hydraulic retention time (HRT), is defined as the quotient of the reactor volume and the input rate of raw waste water. Due to the 1 1 recycle scheme, the stream entering the reactor is twice as large as the input rate of raw waste water, so that the true residence time in the reactor is only 50 percent of the systemic residence time . 

If the mobile phase is compressible, the simple product of the corrected retention time and flow rate will be incorrect, and the corrected retention volume must be taken as the product of the corrected retention time and the mean flow rate. The true corrected retention volume has been shown to be given by [1]... 

Chemical noise is also present in most chemical analyses. This arises from other solutes which give rise to a nonrandom signal at the same retention time as the solute of interest. This noise is much more difficult to discuss and quantitate, as the accurate estimation of this noise would require a true sample blank containing the exact matrix minus the solute of interest. 

The chromatogram contains a wealth of information. It will contain one or more peaks, usually of a slightly asymmetrical, normal Gaussian) distribution (more on this later), indicating when each sample component eluted from the column and was detected. Each component has a retention time tj that is specific for that component, and is reasonably consistent from one day to the next, run under a set of specific chromatographic conditions. The is time of the maximum of the peak and is slighdy longer than the true elution time because of the time delay between when a component actually elutes from the column and... 

The resolution factor is usually estimated from the peak retention times and widths observed in a chromatogram of a mixture of solutes. However, in a rigorous way, a more accurate estimation requires the separate injection of the individual compounds. This is particularly true for closely eluting peaks. It has been established that the retention times measured at the peak apex, and mote so the peak widths, are different if the measurement is made on individually injected solutes or on the peaks in a mixture. This difference is more pronounced when the peak shape cannot be described simply by a Gaussian profile, and where the center of gravity of the peak does not correspond to the peak apex (8). Nevertheless, the chief drawback of the resolution factor Rs is the fact that it does not take into account the relative peak height (9) of the... 

In order to optimize a separation and produce it in the minimum time, the capacity ratios and separation ratios must be measured for a given pair of enantiomers under known conditions of mobile phase composition and temperature (this will be discussed in detail later in this chapter). Unfortunately, when two peaks are eluted close together, which frequently occurs in chiral chromatography, the positions of the peak maxima are distorted due to the immediate presence of the other peak. An example of this problem is shown in figure 10.1, where the peaks are simulated and added, and the composite envelope plotted over the envelope of each individual peak. It is seen that the actual retention difference, if taken from the maxima of the envelope, will give a value of less than 60% of the true retention difference. Unfortunately, this type of error will probably not be taken into account by most data processing software. It follows, that if such data is used in an attempt to calculate the... 

Solvents of equal strength will yield similar k values of the analytes, but in practice the observed retention times and resolutions can differ due to their selectivity properties. As an example, tert-butyl methyl ether and acetonitrile have similar strengths, but the former is basic whereas the latter is not. The same can be true for solvent mixtures. The separation of the two diastereomers shown in Fig. 1 was tried with several mixtures (on LiChrosorb SI 60) and the following results were obtained ... 

The results obtained were probably as accurate and precise as any available and, consequently, were unique at the time of publication and probably unique even today. Data were reported for different columns, different mobile phases, packings of different particle size and for different solutes. Consequently, such data can be used in many ways to evaluate existing equations and also any developed in the future. For this reason, the full data are reproduced in Tables 1 and 2 in Appendix 1. It should be noted that in the curve fitting procedure, the true linear velocity calculated using the retention time of the totally excluded solute was employed. An example of an HETP curve obtained for benzyl acetate using 4.86%v/v ethyl acetate in hexane as the mobile phase and fitted to the Van Deemter equation is shown in Figure 1. 

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